Various communication systems use discrete multi-tone (DMT) signaling, in which the available bandwidth is split into a large number of sub-channels. DMT techniques are based on using many narrow-band carriers, all of which are operating simultaneously. Each narrow-band carrier conveys a small fraction of the total information. The main use of the DMT technique is in the Asymmetrical Digital Subscriber Line (ADSL) modem.
DMT signals suffer from high Peak-to-Average Ratio (PAR), which occurs as a result of the large number of sub-channels required in order to achieve near optimum performance, and large amplitude peak values that occur in the case when all or a substantial number of the sub-channels add constructively. Such high PAR leads to severe constraints on the dynamic range of the line drivers, as well as on the number of bits employed within the Analog-to-Digital Converter (ADC) and the Digital-to-Analog Converter (DAC). Therefore, high resolution linear CODECs (COder/DECoder) are required in order to achieve the desired quantization Signal-to-Noise Ratio (SNR). High resolutions are achieved by a large number of bits.
The article “On the Uniform ADC Bit Precision and Clip Level Computation for a Gaussian Signal” by Noafal Al-Dahir and John M. Cioffi, IEEE Transactions on Signal Processing, Vol. 44, No. 2, February 1996, discloses two analysis methods for computing the required bit precision of the uniform quantizer for multi-carrier input signals of an ADC. The first method fixes the probability of overload and sets the dynamic range of the quantizer to accommodate the worst-case Signal-to-Quantization Noise Ratio (SQNR). In other words, this method ensures that quantization effects do not degrade the SNR by more than a desired value in decibels (dBs). The desired value is reached by restriction of the number of information bits per dimension for each sub-channel and determination of the probability of error.
The second method sets the clipping level (where “clipping” means limiting the signal's maximum amplitude) of the quantizer to meet a desired overload distortion level, using knowledge of the input Probability Density Function (PDF).
The two identified methods use uniform ADC and a bit precision and a clip level computation for Gaussian signals. In both methods, however, high peak-to-average ratios require a large dynamic range from ADC and DAC. Therefore, a large number of bits are required for obtaining the desired quantization SNR.
The article “Analysis of Clipping Effect in DMT Based ADSL Systems” by D. Mestdagh, P. Spruyt and B. Biran, Proc. Int. Conf. Commun., May 1994, discloses the effect of clipping a DMT signal. That publication demonstrates that clipping can reduce the number of bits in the ADC and the DAC, as well as the dynamic range of the line drivers, while keeping the overall SNR the same as without clipping. However, the SQNR remains at a lower value.
All the methods described above, although providing satisfactory gain and, in some instances, a higher SQNR with low bit precision, are not entirely satisfactory. There is, therefore, a need in the art for improving quantization SNR for DMT systems, and particularly for achieving such improvement while retaining the length of the CODEC words and the digital-to-analog (D/A) and analog-to-digital (A/D) bits necessary for a required SQNR.